{"paper":{"title":"On the Convergence of the Variational Iteration Method for Klein-Gordon Problems with Variable Coefficients II","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.NA","math.AP"],"primary_cat":"math.NA","authors_text":"Pavel Drabek, Shohreh Gholizadeh Siahmazgi, Stephen B Robinson","submitted_at":"2024-07-19T15:50:32Z","abstract_excerpt":"In this paper we investigate convergence for the Variational Iteration Method (VIM) which was introduced and described in \\cite{He0},\\cite{He1}, \\cite{He2}, and \\cite{He3}. We prove the convergence of the iteration scheme for a linear Klein-Gorden equation with a variable coefficient whose unique solution is known. The iteration scheme depends on a {\\em Lagrange multiplier}, $\\lambda(r,s)$, which is represented as a power series. We show that the VIM iteration scheme converges uniformly on compact intervals to the unique solution. We also prove convergence when $\\lambda(r,s)$ is replaced by an"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2407.14423","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2407.14423/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}